Localization of elliptic multiscale problems

@article{Mlqvist2014LocalizationOE,
  title={Localization of elliptic multiscale problems},
  author={Axel M{\aa}lqvist and Daniel Peterseim},
  journal={Math. Comput.},
  year={2014},
  volume={83},
  pages={2583-2603}
}
This paper constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying diffusion coefficient. The basis functions are solutions to local problems on vertex patches. The error of the corresponding generalized finite element method decays exponentially with respect to the number of layers of elements in the patches. Hence, on a uniform mesh of size H, patches of diameter H log(1/H) are sufficient to preserve a linear rate of convergence in H… CONTINUE READING
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